NAME
SbMatrix -
The SbMatrix class is a 4x4 dimensional representation of a matrix.
SbMatrix is used by many other classes in Coin. It provides storage for
a 4x4 matrix of single-precision floating point values.
SYNOPSIS
#include <Inventor/SbLinear.h>
Public Member Functions
SbMatrix (void)
SbMatrix (const float a11, const float a12, const float a13, const
float a14, const float a21, const float a22, const float a23, const
float a24, const float a31, const float a32, const float a33, const
float a34, const float a41, const float a42, const float a43, const
float a44)
SbMatrix (const SbMat &matrix)
SbMatrix (const SbMat *matrix)
~SbMatrix (void)
SbMatrix & operator= (const SbMat &m)
operator float * (void)
SbMatrix & operator= (const SbMatrix &m)
void setValue (const SbMat &m)
void setValue (const class SbDPMatrix &m)
const SbMat & getValue (void) const
void makeIdentity (void)
void setRotate (const SbRotation &q)
SbMatrix inverse (void) const
float det3 (int r1, int r2, int r3, int c1, int c2, int c3) const
float det3 (void) const
float det4 (void) const
SbBool equals (const SbMatrix &m, float tolerance) const
operator SbMat & (void)
float * operator[] (int i)
const float * operator[] (int i) const
SbMatrix & operator= (const SbRotation &q)
SbMatrix & operator*= (const SbMatrix &m)
void getValue (SbMat &m) const
void setScale (const float s)
void setScale (const SbVec3f &s)
void setTranslate (const SbVec3f &t)
void setTransform (const SbVec3f &t, const SbRotation &r, const SbVec3f
&s)
void setTransform (const SbVec3f &t, const SbRotation &r, const SbVec3f
&s, const SbRotation &so)
void setTransform (const SbVec3f &translation, const SbRotation
&rotation, const SbVec3f &scaleFactor, const SbRotation
&scaleOrientation, const SbVec3f ¢er)
void getTransform (SbVec3f &t, SbRotation &r, SbVec3f &s, SbRotation
&so) const
void getTransform (SbVec3f &translation, SbRotation &rotation, SbVec3f
&scaleFactor, SbRotation &scaleOrientation, const SbVec3f ¢er)
const
SbBool factor (SbMatrix &r, SbVec3f &s, SbMatrix &u, SbVec3f &t,
SbMatrix &proj)
SbBool LUDecomposition (int index[4], float &d)
void LUBackSubstitution (int index[4], float b[4]) const
SbMatrix transpose (void) const
SbMatrix & multRight (const SbMatrix &m)
SbMatrix & multLeft (const SbMatrix &m)
void multMatrixVec (const SbVec3f &src, SbVec3f &dst) const
void multVecMatrix (const SbVec3f &src, SbVec3f &dst) const
void multDirMatrix (const SbVec3f &src, SbVec3f &dst) const
void multLineMatrix (const SbLine &src, SbLine &dst) const
void multVecMatrix (const SbVec4f &src, SbVec4f &dst) const
void print (FILE *fp) const
Static Public Member Functions
static SbMatrix identity (void)
Friends
SbMatrix operator* (const SbMatrix &m1, const SbMatrix &m2)
int operator== (const SbMatrix &m1, const SbMatrix &m2)
int operator!= (const SbMatrix &m1, const SbMatrix &m2)
Detailed Description
The SbMatrix class is a 4x4 dimensional representation of a matrix.
SbMatrix is used by many other classes in Coin. It provides storage for
a 4x4 matrix of single-precision floating point values.
By definition, matrices in Coin should be set up in column-order mode.
This is the same order as used by e.g. OpenGL, but note that books on
geometry often uses the opposite row-order mode, which can confuse new-
comers to the API.
Another way to think of column-order matrices is that they use post-
order multiplications: that is, to concatenate a transformation from a
second matrix with your current matrix, it should be multiplied on the
right-hand side, i.e. with the SbMatrix::multRight() method.
If you have a matrix in row-order from some other source, it can be
’converted’ to column-order by transposing it with
SbMatrix::transpose(). A simple example will help to explain this.
With row-order matrices, a transformation matrix with position,
rotation and scale looks like this:
M = T * R * S
Where T is translation, R is rotation and S is the scale. What this
means is that scale is applied first. The scaled matrix is then
rotated, and finally the scaled and rotated matrix is translated. When
using column-order matrices, as done in Coin, matrices are represented
slightly differently; the order of multiplication is reversed:
M = S * R * T
The transformation is just the same as the row-order matrix. The only
difference being the order of multiplication. To understand why this is
so, consider the sample transformation:
M = T * R * S
Converting M from a row-order matrix to a column-order matrix is done
as follows:
M^t = (T * R * S)^t
M^t = ((T * R) * S)^t
M^t = S^t * (T * R)^t
M^t = S^t * R^t * T^t
All left to be done is to remove the transpose symbols, and the
matrices have been converted to column-order matrices:
M = S * R * T
This was done using the fact that:
A^t = (B * C)^t = C^t * B^t
Converting from column-order to row-order is done using the same
principle.
Constructor & Destructor Documentation
SbMatrix::SbMatrix (void) The default constructor does nothing. The matrix
will be uninitialized.
SbMatrix::SbMatrix (const float a11, const float a12, const float a13,
const float a14, const float a21, const float a22, const float a23,
const float a24, const float a31, const float a32, const float a33,
const float a34, const float a41, const float a42, const float a43,
const float a44) Constructs a matrix instance with the given initial
elements.
SbMatrix::SbMatrix (const SbMat & matrixref) Constructs a matrix instance
with the initial elements from the matrix argument.
SbMatrix::SbMatrix (const SbMat * matrixptr) This constructor is courtesy
of the Microsoft Visual C++ compiler.
SbMatrix::~SbMatrix (void) Default destructor does nothing.
Member Function Documentation
SbMatrix & SbMatrix::operator= (const SbMat & m) Assignment operator.
Copies the elements from m to the matrix.
SbMatrix::operator float * (void) Return pointer to the matrix’ 4x4 float
array.
SbMatrix & SbMatrix::operator= (const SbMatrix & m) Assignment operator.
Copies the elements from m to the matrix.
void SbMatrix::setValue (const SbMat & m) Copies the elements from m into
the matrix.
See also:
getValue().
const SbMat & SbMatrix::getValue (void) const Returns a pointer to the 2
dimensional float array with the matrix elements.
See also:
setValue().
void SbMatrix::makeIdentity (void) Set the matrix to be the identity
matrix.
See also:
identity().
void SbMatrix::setRotate (const SbRotation & q) Set matrix to be a rotation
matrix with the given rotation.
See also:
setTranslate(), setScale().
SbMatrix SbMatrix::inverse (void) const Return a new matrix which is the
inverse matrix of this.
The user is responsible for checking that this is a valid operation to
execute, by first making sure that the result of SbMatrix::det4() is
not equal to zero.
float SbMatrix::det3 (int r1, int r2, int r3, int c1, int c2, int c3) const
Returns the determinant of the 3x3 submatrix specified by the row and
column indices.
float SbMatrix::det3 (void) const Returns the determinant of the upper left
3x3 submatrix.
float SbMatrix::det4 (void) const Returns the determinant of the matrix.
SbBool SbMatrix::equals (const SbMatrix & m, float tolerance) const Check
if the m matrix is equal to this one, within the given tolerance value.
The tolerance value is applied in the comparison on a component by
component basis.
SbMatrix::operator SbMat & (void) Return pointer to the matrix’ 4x4 float
array.
float * SbMatrix::operator[] (int i) Returns pointer to the 4 element array
representing a matrix row. i should be within [0, 3].
See also:
getValue(), setValue().
const float * SbMatrix::operator[] (int i) const Returns pointer to the 4
element array representing a matrix row. i should be within [0, 3].
See also:
getValue(), setValue().
SbMatrix & SbMatrix::operator= (const SbRotation & q) Set matrix to be a
rotation matrix with the given rotation.
See also:
setRotate().
SbMatrix & SbMatrix::operator*= (const SbMatrix & m) Right-multiply with
the m matrix.
See also:
multRight().
void SbMatrix::getValue (SbMat & m) const Return matrix components in the
SbMat structure.
See also:
setValue().
SbMatrix SbMatrix::identity (void) [static] Return the identity matrix.
See also:
makeIdentity().
void SbMatrix::setScale (const float s) Set matrix to be a pure scaling
matrix. Scale factors are specified by s.
See also:
setRotate(), setTranslate().
void SbMatrix::setScale (const SbVec3f & s) Set matrix to be a pure scaling
matrix. Scale factors in x, y and z is specified by the s vector.
See also:
setRotate(), setTranslate().
void SbMatrix::setTranslate (const SbVec3f & t) Make this matrix into a
pure translation matrix (no scale or rotation components) with the
given vector as the translation.
See also:
setRotate(), setScale().
void SbMatrix::setTransform (const SbVec3f & t, const SbRotation & r, const
SbVec3f & s) Set translation, rotation and scaling all at once. The
resulting matrix gets calculated like this:
M = S * R * T
where S, R and T is scaling, rotation and translation matrices.
See also:
setTranslate(), setRotate(), setScale() and getTransform().
void SbMatrix::setTransform (const SbVec3f & t, const SbRotation & r, const
SbVec3f & s, const SbRotation & so) Set translation, rotation and
scaling all at once with a specified scale orientation. The resulting
matrix gets calculated like this:
M = Ro-¹ * S * Ro * R * T
where Ro is the scale orientation, and S, R and T is scaling, rotation
and translation.
See also:
setTranslate(), setRotate(), setScale() and getTransform().
void SbMatrix::setTransform (const SbVec3f & translation, const SbRotation
& rotation, const SbVec3f & scaleFactor, const SbRotation &
scaleOrientation, const SbVec3f & center) Set translation, rotation and
scaling all at once with a specified scale orientation and center
point. The resulting matrix gets calculated like this:
M = -Tc * Ro-¹ * S * Ro * R * T * Tc
where Tc is the center point, Ro the scale orientation, S, R and T is
scaling, rotation and translation.
See also:
setTranslate(), setRotate(), setScale() and getTransform().
void SbMatrix::getTransform (SbVec3f & t, SbRotation & r, SbVec3f & s,
SbRotation & so) const Factor the matrix back into its translation,
rotation, scale and scaleorientation components.
See also:
factor()
void SbMatrix::getTransform (SbVec3f & translation, SbRotation & rotation,
SbVec3f & scaleFactor, SbRotation & scaleOrientation, const SbVec3f &
center) const Factor the matrix back into its translation, rotation,
scaleFactor and scaleorientation components. Will eliminate the center
variable from the matrix.
See also:
factor()
SbBool SbMatrix::LUDecomposition (int index[4], float & d) This function
produces a permuted LU decomposition of the matrix. It uses the common
single-row-pivoting strategy.
FALSE is returned if the matrix is singular, which it never is, because
of small adjustment values inserted if a singularity is found (as Open
Inventor does too).
The parity argument is always set to 1.0 or -1.0. Don’t really know
what it’s for, so it’s not checked for correctness.
The index[] argument returns the permutation that was done on the
matrix to LU-decompose it. index[i] is the row that row i was swapped
with at step i in the decomposition, so index[] is not the actual
permutation of the row indexes!
BUGS: The function does not produce results that are numerically
identical with those produced by Open Inventor for the same matrices,
because the pivoting strategy in OI was never fully understood.
See also:
SbMatrix::LUBackSubstitution
void SbMatrix::LUBackSubstitution (int index[4], float b[4]) const This
function does a solve on the ’Ax = b’ system, given that the matrix is
LU-decomposed in advance. First, a forward substitution is done on the
lower system (Ly = b), and then a backwards substitution is done on the
upper triangular system (Ux = y).
The index[] argument is the one returned from
SbMatrix::LUDecomposition(), so see that function for an explanation.
The b[] argument must contain the b vector in ’Ax = b’ when calling the
function. After the function has solved the system, the b[] vector
contains the x vector.
BUGS: As is done by Open Inventor, unsolvable x values will not return
NaN but 0.
SbMatrix SbMatrix::transpose (void) const Returns the transpose of this
matrix.
SbMatrix & SbMatrix::multRight (const SbMatrix & m) Let this matrix be
right-multiplied by m. Returns reference to self.
This is the most common multiplication / concatenation operation when
using column-order matrices, as SbMatrix instances are, by definition.
See also:
multLeft()
SbMatrix & SbMatrix::multLeft (const SbMatrix & m) Let this matrix be left-
multiplied by m. Returns reference to self.
(Be aware that it is more common to use the SbMatrix::multRight()
operation, when doing concatenation of transformations, as SbMatrix
instances are by definition in column-order, and uses post-
multiplication for common geometry operations.)
See also:
multRight()
void SbMatrix::multMatrixVec (const SbVec3f & src, SbVec3f & dst) const
Multiply src vector with this matrix and return the result in dst.
Multiplication is done with the vector on the right side of the
expression, i.e. dst = M * src.
(Be aware that it is more common to use the SbMatrix::multVecMatrix()
operation, when doing vector transformations, as SbMatrix instances are
by definition in column-order, and uses post-multiplication for common
geometry operations.)
See also:
multVecMatrix(), multDirMatrix() and multLineMatrix().
void SbMatrix::multVecMatrix (const SbVec3f & src, SbVec3f & dst) const
Multiply src vector with this matrix and return the result in dst.
Multiplication is done with the vector on the left side of the
expression, i.e. dst = src * M.
It is safe to let src and dst be the same SbVec3f instance.
This method can be used (using the current model matrix) to transform a
point from an object coordinate systems to the world coordinate system.
This operation is what you would usually do when transforming vectors,
as SbMatrix instances are, by definition, column-order matrices.
See also:
multMatrixVec(), multDirMatrix() and multLineMatrix().
void SbMatrix::multDirMatrix (const SbVec3f & src, SbVec3f & dst) const
Multiplies src by the matrix. src is assumed to be a direction vector,
and the translation components of the matrix are therefore ignored.
Multiplication is done with the vector on the left side of the
expression, i.e. dst = src * M.
See also:
multVecMatrix(), multMatrixVec() and multLineMatrix().
void SbMatrix::multLineMatrix (const SbLine & src, SbLine & dst) const
Multiplies line point with the full matrix and multiplies the line
direction with the matrix without the translation components.
See also:
multVecMatrix(), multMatrixVec() and multDirMatrix().
void SbMatrix::multVecMatrix (const SbVec4f & src, SbVec4f & dst) const
This is an overloaded member function, provided for convenience. It
differs from the above function only in what argument(s) it accepts.
void SbMatrix::print (FILE * fp) const Write out the matrix contents to the
given file.
Friends And Related Function Documentation
SbMatrix operator* (const SbMatrix & m1, const SbMatrix & m2) [friend]
Multiplies matrix m1 with matrix m2 and returns the resultant matrix.
int operator== (const SbMatrix & m1, const SbMatrix & m2) [friend] Compare
matrices to see if they are equal. For two matrices to be equal, all
their individual elements must be equal.
See also:
equals().
int operator!= (const SbMatrix & m1, const SbMatrix & m2) [friend] Compare
matrices to see if they are not equal. For two matrices to not be
equal, it is enough that at least one of their elements are unequal.
See also:
equals().
Author
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